This notion might appear obscure to the reader unfamiliar with categorical logic; [1]} contains lots of examples to help the reader build their intuition: for instance, an object of the category of sets is finitely presentable if and only if it is finite, and a (commutative) monoid is finitely presentable if and only if it admits a presentation \(\langle G\mid R\rangle \)  where both \(G\)  (set of generators) and \(R\)  (set of relations) are finite sets: this happens for many other algebraic structures, and thus motivates the definition.
